Hello Lindy,
I would suggest 2 possibilities, and a third, very outside chance;
I have discounted the posibility that a mistake was made at the Registration, as I would expect her daughter to notice, and query it at the time.
1) if you have a copy or later issued death certificate, rather than the original contemporanous one (issued during the process of registration - anything after this, even just a week later is a 'copy' officially), or are working from a transcript, then it is possible that the original entry in the register has been mis-read.
2) When registering the death, her daughter provided an original birth certificate or other document which bore her 'real' name, rather than what the family had always known her by.
3) when registering the death, her daughter provided a copy of a document with the wrong name on it - but I think this would have been noticed at the time too.
I have several examples of (2) in my family:
a) My great-aunt was in hospital, but the ward would not admit it to my father (her nephew), because he only knew her as 'Megan', and her real name was 'Mary';
b) my Great-uncle told how he used to visit as a child to his 'Auntie Lizzie'. In her grandfather's will she is referred to as 'Elizabeth'. On the 1881 Census, her father has named her 'Lilly' with 2 'L's. On a sampler she embroidered whilst in the orphanage referred to in the will just mentioned, she identified herself (she was about 14) as 'Lily' with a single 'L'.
c) my mother had aunts who were not, at birth, named Molly, Polly, Dolly, but these were the names used throughout.
d) I would add that in your example, whilst Nancy and Mary are definitely names, 'Nannie' could be a name or a designation, like 'Grandma'. Nan, Nana, Nanny, or Nannie is a common name for 'Grannie' in south Wales, possibly elsewhere. My father had a 'Grandma' Church, and a 'Nana' Sanderson - because they had the same first name. I myself had a Grandad Lily and a Grandad Edna, because they both had the same first name, and I already shared my father's Nana.